The segmentation of an object and the determination of the volume of a segmented object are particularly important in the diagnosis and treatment of cancer, for example, of lung cancer.
Since the entire cardiac output flows through the lungs, the risk of hematogenous lung metastases is very high. Apart from primary lung cancer, the most common tumors metastasizing in the lungs are breast cancer, gastrointestinal tumors, kidney cancer, melanoma, sarcomas, lymphomas, leukemias, and germ cell tumors. Because of the systemic character of the disease, chemotherapy is the standard treatment for lung metastases. To assess the effect of chemotherapy, a follow-up examination is performed typically three to six months after the start of the treatment. Tumor growth is one of the standard decision parameters for therapy success.
Lung cancer, i.e. the primary bronchial carcinoma, is the leading cause of cancer death, and early detection is crucial to the chance for curative treatment. However, early stage lung cancer patients are usually asymptomatic. To allow sufficiently early detection, efforts are under way to establish lung cancer screening using multi-detector CT for populations at risk such as smokers, or asbestos exposed coal mine workers. A major problem with lung cancer screening is that small nodules are detected in the majority of subjects, which are benign in most cases. Again, nodule growth is the standard parameter for the discrimination between benign and malignant nodules. A follow-up scan is performed for patients with suspicious lesions typically three to six month later. Exact growth assessment is crucial for correct classification, allowing for more reliable detection of malignancy.
Since most nodules grow irregularly in three dimensions, the assessment of nodule growth requires three-dimensional measurements. Only with the advent of multi-detector CT scanners it became possible to scan the thorax in an approximately isotropic three-dimensional resolution without significant breathing artifacts. But even on current high resolution scans, accurate volume assessment is virtually impossible for the radiologist without substantial computer assistance. Hence, axial diameters were traditionally used for estimation of volumetric nodule growth. For example, in the context of therapy monitoring, current standard criteria (for example RECIST, published in “New guidelines to evaluate the response to treatment in solid tumors. European organization for research and treatment of cancer, national cancer institute of the United States, national cancer institute of Canada”, P. Therasse et al., J. Natl. Cancer Inst., vol. 92, no. 3, pp. 205-216, February 2000) require the radiologist to locate the five largest tumors in the lung and find the axial slice where the tumor appears largest in order to manually measure the greatest nodule diameter. Strength and weaknesses of the RECIST method in face of emerging volumetric quantification methods are discussed elaborately in “Evaluation of the response to treatment of solid tumours—a consensus statement of the international cancer imaging society”, J. E. Husband et al., British J. of Cancer, vol. 90, pp. 2256-2260, May 2004. Even if measuring errors are neglected, these two-dimensional criteria are reliable only for spherical nodules and unsuited for irregularly shaped nodules. Additionally, manually finding the correct slice and measuring two-dimensional diameters for each of possibly many nodules not only leads to reproducibility issues but is also time consuming. In order to assess nodule growth quickly and reliably, computer assistance in volume measurements is desirable.
Known segmentation methods have often the drawback that they cannot segment high-density objects which are connected to other high-density structures. For example, solid pulmonary lesions generally show a high density contrast to the surrounding lung parenchyma in CT scans. The major difficulty in three-dimensional segmentation of lung lesions is that most nodules are directly connected to other high density structures. Even in contrast enhanced CT scans, it is in most cases impossible to separate a lesion from connected vasculature or the chest wall solely based on density contrast.
Furthermore, known segmentation methods have often the problem that they cannot segment objects of different size with the same quality, i.e. with the same reproducibility and accuracy. This is particularly important in cancer diagnostic and treatment, because lesions discovered during screening of an asymptomatic population are mostly either small benign nodules, or early stage lung cancer. They are generally lesser in size and usually not extensively interconnected with vasculature. In contrast to this, the population of patients undergoing chemotherapy typically suffers from advanced inoperable cancer. Metastatic tumors occur at all stages, so that segmentation algorithms have to deal with the full range of appearances, from small spherical nodules (Ø<10 mm) consisting mostly of partial volume voxels, to large nodules (Ø>40 mm) of irregular morphology. Due to their size, the latter are more likely to be complexly connected to vasculature and chest wall.
In addition, known segmentation methods are computational complex and, therefore, slow. In particular, in the field of cancer diagnostic and treatment the clinical usefulness of a method highly depends on its speed. Especially for larger lesions, the computational performance of a segmentation algorithm is a critical issue, since the volume of interest to be analyzed for, for example, a 40 mm tumor is about 64 times larger than for a 10 mm nodule.
In the following some known methods of segmentation and of determination of the volume of a segmented object will be discussed.
Before modern multi-detector CT scanners were widely available, slice-based approaches were introduced. Xu et al. developed a method which performs dynamic programming on a slice-by-slice basis using manual initialization and shape constraints (published in “Automated lung nodule segmentation using dynamic programming and EM-based classification”, N. Xu et al., Proc. SPIE Med. Imag., vol. 4684, 2002, pp. 666-676).
In a method described by Fan et al., a thresholding is followed by an analysis of the nodule's orientation and size, and the adaptation of a three-dimensional template (published in “Automatic segmentation of pulmonary nodules by using dynamic 3d cross-correlation for interactive CAD systems”, L. Fan et al., Proc. SPIE Med. Imag., vol. 4684, May 2002, pp. 1362-1369). The method is suitable for small, approximately ellipsoid nodules and requires interactive correction in case of irregularly shaped nodules. However, for nodules attached to the chest wall, an ellipsoid shape is usually not a good approximation.
An approach by Kostis et al. was designed for small pulmonary nodules and uses a semi-automatic classification of the target nodule into one of four nodule models, the most important ones representing solitary, vascularized, and juxtapleural nodules (published in “Three-dimensional segmentation and growth rate estimation of small pulmonary nodules in helical CT images”, W. J. Kostis et al., IEEE Trans. Med. Imag., vol. 22, no. 10, pp. 1259-1274, 2003). After an initial segmentation using a fixed threshold, separation from adjacent high density structures is performed by morphological methods. This method is specifically designed for small nodules. Several assumptions are made concerning especially the removal of attached vasculature that are not transferable to objects, for example, lesions, of arbitrary size and morphology.
In “Robust anisotropic gaussian fitting for volumetric characterization of pulmonary nodules in multislice CT”, IEEE Trans. Med. Imag., vol. 24, no. 3, pp. 409-423, March 2005, Okada et al. presented an automated method to approximate solid nodules as well as Ground Glass Opacities (GGO) by ellipsoids using anisotropic Gaussian fitting. The volume of the nodule was estimated by the volume of the ellipsoid. While the approach is intriguing due to its applicability to non-solid nodules, the question of volumetric reproducibility for nodules of non-elliptical shape, especially in case shape changes due to irregular nodule growth, is a potential drawback of this ellipsoid approximation approach.
Fetita et al. presented a complete Computer Aided Detection (CAD) system, which also included the segmentation of detected nodules (published in “3d automated lung nodule segmentation in HRCT”, C. I Fetita et al., Proc. MICCAI, 2003, pp. 626-634). This system is specifically designed for small nodules and uses initial thresholding followed by morphological methods for segmentation. In contrast to the other approaches discussed here, it can take advantage of global information acquired during the detection procedure which processes the complete lungs. While the global information can considerably help in assessing the local situation more accurately, an analysis of the complete lung implies the analysis of 300 to 500 CT slices and is not suitable for fast, interactive one-click methods unless a preprocessing step was performed earlier. Any dependence on a preprocessing step makes it harder to integrate a method as a plug-in to existing workstations or CAD systems.
After an object has been segmented, it is often required to determine the volume of the segmented object. The process of determining of the volume is called volumetry. A major issue in the volumetry of objects, in particular of small objects, is the so-called partial volume effect. Due to the limited resolution of an imaging device, for example, of a CT scanner a single voxel may represent more than a single part, for example tissue type, at a time, and the measured density is dependent on the individual densities of this part of the object and the volume ratio of this part within the voxel. While the amount of this particular partial volume effect depends primarily on the scanner resolution, additional volume averaging occurs during image reconstruction, which is affected by parameters such as reconstruction kernel and slice thickness.
It is a well-known fact that these averaging effects cause a substantial sensitivity of two-dimensional diameter as well as three-dimensional volume measurements to changes in scanning or reconstruction protocols when derived straight-forward from segmentation results. In particular, in a typical clinical setting this is a significant problem, because it is often not possible to guarantee that a follow-up scan is performed with the same reconstruction and scanning protocol—or even at the same scanner—as the previous scan, which usually dates back between three and 24 months.
In most of the publications of methods of segmentation discussed above, volumetry is given as the primary motivation for segmenting objects, in particular lung nodules. However, the step from segmentation to volume assessment is often not explicitly discussed, implying that by solving the problem of segmentation, the problem of volumetry could be considered solved as well. No evaluation of reproducibility with respect to varying acquisition or reconstruction parameters was performed in any of the publications. Current scientific methods as well as commercial products available for the assessment of lung nodule volume were shown to be associated with significant impairment of reproducibility when acquisition or reconstruction parameters were varied (see, for example, “Small pulmonary nodules: Volume measurement at chest CT—phantom study”, J. P. Ko et al., Radiology, vol. 228, no. 3, pp. 864-870, 2003; “Pulmonary metastases: effect of CT section thickness on measurement-initial experience”, B. Zhao et al., Radiology, vol. 234, no. 3, pp. 934-939, 2005; and “Volumetric measurement of synthetic lung nodules with multi-detector row cc Effect of various image reconstruction parameters and segmentation thresholds on measurement accuracy”, J. M. Goo et al., Radiology, vol. 235, no. 3, pp. 850-856, June 2005).
Volumes are generally extracted by summing up the volume of segmented voxels, which were obtained using a segmentation method that uses thresholding at least in order to generate an initial approximation of the nodule shape. When applied to small objects whose boundaries are subject to volume averaging, the measured volumes will depend highly on its amount. Volume averaging occurs wherever there is a density gradient in the voxels, for example, in CT data, such as between the nodule tissue and the lung parenchyma. Causes for volume averaging are not only the limited physical scanning resolution (the classical partial volume effect), but also the reconstructed resolution (field of view, slice thickness) and the filter algorithm used for reconstruction, which serves as low-pass filtering in order to reduce noise. Whenever any of these parameters is varied, conventional, threshold-based volume assessment will be affected. Volume averaging leads to nodule volume underestimation by threshold based methods. This is mostly due to the compact, mostly convex shape of lung nodules: The average boundary voxel is surrounded by voxels with more parenchyma than nodule tissue. In addition to different averaging strengths, density variations of either nodule (e. g., due to calcification processes or contrast agent) or surrounding parenchyma (e. g., due to different inspiration state) can significantly influence fixed threshold-based volumetry.
First attempts have been made to reduce the impact of the partial volume and reconstruction-based volume averaging effects by supersampling prior to segmentation (published in “Three-dimensional segmentation and growth rate estimation of small pulmonary nodules in helical CT images”, W. J. Kostis et al., IEEE Trans. Med. Imag., vol. 22, no. 10, pp. 1259-1274, 2003), by applying compensatory equations to measured volumes (published in “Effect of varying CT section width on volumetric measurement of lung tumors and application of compensatory equations”, H. T. Winer-Muram et al., Radiology, vol. 229, no. 1, pp. 184-194, 2003), and by histogram analysis without previous segmentation (published in “Small pulmonary nodules: Volume measurement at chest CT—phantom study”, J. P. Ko et al., Radiology, vol. 228, no. 3, pp. 864-870, 2003). These attempts will be discussed in the following. Kostis et al. address in “Three-dimensional segmentation and growth rate estimation of small pulmonary nodules in helical CT images”, W. J. Kostis et al., IEEE Trans. Med. Imag., vol. 22, no. 10, pp. 1259-1274, 2003 the partial volume effect. In this publication an upper bound for the error induced by discrete sampling of a perfect circle was computed. It was shown that the volumetric error produced by misclassification of boundary voxels converges against zero with increasing scanner resolution for this setting, an effect, which can be shown in the three-dimensional case as well. However, volume averaging problems cannot be completely overcome by supersampling the data sufficiently. The error bound computations base on an arbitrary sampling of a noiseless, continuous image. This situation describes the scanning process only and neglects the effects of reconstruction. Any postprocessing algorithms are performed on the reconstructed images, and reconstructed images are already quantized. Hence, volume averaging has already taken place, and this loss of information cannot be reversed by supersampling.
An approach for counteracting imaging parameter induced variabilities is to determine compensatory equations for the measured volumes by explicitly incorporating information about the acquisition and reconstruction. Winer-Muram et al. attempted to compensate for volumetric deviations caused by slice thickness variations by performing affine transformations of the measured volumes, which were initially obtained by manual measurements (published in “Effect of varying CT section width on volumetric measurement of lung tumors and application of compensatory equations”, H. T. Winer-Muram et al., Radiology, vol. 229, no. 1, pp. 184-194, 2003). But this approach cannot reliably consider all parameters—from the physical scanner resolution to the patient's inspiration state—which can result in measured volume changes for actually unchanged nodules.
Alternatively to fixed threshold approaches, adaptive thresholding (also called variable thresholding) could be used. As part of the study in “Small pulmonary nodules: Volume measurement at chest CT—phantom study”, J. P. Ko et al., Radiology, vol. 228, no. 3, pp. 864-870, 2003, Ko et al. compared the reproducibility of fixed and variable thresholding for isolated phantom nodules, showing a significantly better performance of the variable threshold technique. For in vivo nodules, however, finding the correct threshold that leads to accurate and reproducible volumetry prior to segmentation is significantly more difficult. Firstly, in the instant where the threshold needs to be determined, no segmentation is available. Hence, other high density structures within the volume of interest (VOI) and possibly even connected to the nodule (e.g., chest wall, vasculature) cannot be explicitly excluded, influencing threshold determination mechanisms such as Otsu thresholding (published in “A threshold selection method from gray-level histogram”, N. Otsu, IEEE Trans. Syst. Sci. Cybernetics, vol. 9, no. 1, pp. 62-66, 1979). Secondly, for small nodules where the reconstructed image does not contain even a single voxel representing pure nodule tissue, the method presented by Ko et al. yields volumetry results of a quality which is not sufficient for medical purposes.
In the above mentioned publication of Ko et al., an application of a partial volume analysis approach in the context of lung nodules was proposed. Using no segmentation and only a reference region within the nodule core manually drawn on a central slice, mean densities of pure nodule tissue and surrounding parenchyma were estimated from the data. The volume was computed for each slice by summing up voxel densities in each slice and weighting them with respect to those pure tissue means. In the publication of Ko et al., the evaluation for solid, isolated phantom nodules showed a reproducibility of their so-called Partial Volume Method that was even superior to the one of the variable thresholding technique. While these studies proved the enormous potential of a more elaborate density analysis on the image data set, for example, on a CT image, their method is not suitable for in vivo nodule assessment, since attached high-density structures would be accounted to the nodule volume. In addition, the extraction of mean attenuations for both nodule and parenchyma needs to be performed fully automatic, and still be robust and reliable and undisturbed by other lung structures present within the VOI.